Expert: Richard J. Raridon - 12/19/2008

Question
QUESTION: x+4/3x+2 - x+4/3x+2=
x+4-x+4/3x+2=
8/3x+2=
4/3x=
1 1/3x

Is this correct or did I go to far in simplifying it to the lowest term?

ANSWER: It's really 8/(3x+2) and that's as far as you can go

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QUESTION: Okay,
In my original problem, do I need to change all my signs in the second term since I am using subtraction
example: instead of saying x+4/3x+2, I would say x-4/3x-2. If that's the case my answer would be 1/(3x+2)

ANSWER: Well, it's obvious that the first term is (x+4)/(3x+2).  However,
the second term is not clear.  Do you mean -(x+4)/(3x+2)
or +(-x+4)/(3x+2).  If it's the first way, your final answer is 0.  
If it's the second way then you have 8/(3x+2).  In no case can you get 1/(3x+2)

---------- FOLLOW-UP ----------

QUESTION: I did come up with the second answer. In the rules of polynomials it states that when you are subtracting or have a negative sign between the two terms, you have to change all the signs(opposites) on the second term.My professor questioned me about changing my signs. She let me know that's what I needed to do. I don't agree with that because in my textbook none of the examples on rational exressions states anything about changing signs;only when you simplify polynomials. That's how I came up with answer 1/(3x+2)because I changed all the signs to it's opposite. (-x-4/(3x-2). Ithen continued to work the problem out. I'm just trying to find out the correct way. My professor hasn't contacted me back on this one.

Answer
Even if you would say x-4/3x-2, which is not the same as your original statement, you could cancel the 4's but that leaves you 2x and not 1. If your answer were correct you should be able to put some value for x in the original expressions, add them and get the same answer as putting that value for x in your answer.  You can't do that with 1/(3x+2).  Maybe your professor has been busy and hasn't had a chance to find your error.